Here quotient is 25 so new divisor 2 x 25= 50 and the new dividend is 2500. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. ∴ √9216 = 2 × 2 × 2 × 2 × 2 × 3 = 25.5 (approximate value). Here ( 2nd part of the number)  70 < 72 . So our final answer is √650 =  25.49 = 25.5. AM, GM and HM, Harmonic Progression Formula, Properties and Harmonic Mean Formula, Geometric progression problems and solutions with Formulas and properties, Geometric Progression Formulas and Properties & Sum of Geometric Series, If last digit of perfect Square number =1, last digit of, If last digit of perfect Square number =4 , last digit of, If last digit of perfect Square number =9, last digit of. Bring down the next pair of digits and this becomes the new dividend. If last digit of perfect Square number =5, last digit of Square root for that number=5. If the 2nd part of the number is high then take big number. = 6 × 15 Learn Science with Notes and NCERT Solutions, Chapter 6 Class 8 Squares and Square Roots. = 4 × 5 i.e When a number is multiplied by itself to give the square of number then that number is a square root for that square number. Last updated at Sept. 11, 2018 by Teachoo, Subscribe to our Youtube Channel - https://you.tube/teachoo, Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. Speed Math Division Shortcut tricks Division shortcuts are very much helpful to save time in all our exams. Step V: Find the product of factors obtained in step IV. Cube Root formula of Perfect Cubes of 1 to 100 | Cube root formula in math, Easy Addition and Subtraction Tricks | Shortcut Process for addition, Shortcuts for Multiplication of numbers | Easy way for Multiplications, Percentage formulas while increase and decrease percent of a number, Easiest way to find square of a 2 digit number | Shortcut trick for Square, Shortcut Methods for finding the Cube of a number | number cube tricks, Shortcuts methods of Division math | Tips and tricks for math division, Hi friends Thanks for reading. c) Short cut trick for find the square root for perfect square number. (v) 7744 By prime Factorization, ∴ √5929 = 2 × 3 × 3 × 5 Step1 : Write given number into prime factors. Save my name, email, and website in this browser for the next time I comment. Find the Square root of 576 by prime factorization method. (i) Decompose the number inside the square root into prime factors. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. Step 1 : The given number to be group the digits in pairs, and the remaining digit (if any) is called a period. Find the Square Root of  1009. The new divisor is obtained by taking two times the quotient. Square root of 729 = 3 × 3 × 3 If last digit of perfect Square number =6, last digit of Square root for that number=4 or 6. = 9 × 3 529 = 23 × 23 perfect square closest to 1009 is 32; we will take square root of 1024 i.e. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. Approximate Square Root of any number which is not a Perfect square. Step 2 : Leave the first two digits and take the next remaining digits. You can use this feature to calculate the result of the division of natural numbers by 7 without a calculator quickly. 25 in this calculations, perfect square closest to 1009 is 32; we will take square root of 1024 i.e. = 90. = 98 ∴ √4096= 2 × 2 × 2 × 2 × 2 × 2 Step 5 : Take the second digit in square root (i.e 2 ) and multiply it by next preceding number (i.e 2 x 3 = 6 ). (x) 8100 Here Square the 2, giving 4, and Square the 3, giving 9. = 77 ∴ √5929 = 7 × 11 = 2 × 21 Here 7 > 6 . Here quotient is 2 so new divisor 2 x 2 = 4 and the new dividend is 250. Step 3 : Now take Subtract the product of the divisor and the quotient  (i.e 2 x 2 = 4) from the first period or pair ( i.e 4). d) Approximate Square Root of any number which is not a Perfect square. Step2 : Make pairs of similar factors. Teachoo is free. It is the lowest natural number that cannot be represented as the sum of the squares of three integers. (ii) Inside the square root, for every two same numbers multiplied, one number can be taken out of the square root. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors. Step 4 : Square root of  7056 is 84 or 86. = 2 × 49 Step 4: Now, the new divisor is obtained by taking two times the quotient. I Hope you liked it. = 32 – [ (1024-1009) / (2 x 32) ] The single digit is to be choose like the product of  that product of the new divisor and the this single digit to be equal to or just less than the new dividend. (ii) Make the pair of similar factors such that the both factors in each pair are equal. Here remaining the number is ” 7″. Here our next digit of square root is ” 2 “. Give feed back, comments and please don’t forget to share it. ∴ √9604 = 2 × 7 × 7 Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. Here explain with example in step by step. Step 5 : Take the second digit in square root (i.e 8 ) and multiplying it, by next preceding number (i.e 8 x 9 = 72 ). My self Sivaramakrishna Alluri. ∴ √7744 = 2 × 2 × 2 × 11 Step 2 : Find the largest number whose square is equal to or just less than the first period or pair. 4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Step 3 : Find the less square number for ” 70″ . Bring down the next pair of digits and this becomes the new dividend. Square Root of a Perfect Square by using the Prime Factorization Method. = 88 Finally the quotient so obtained is the required square root of the given number. = 25 +[ (650-625) / (2 x 25) ] Here our given number 650. Example : Find the Square root of 576 by prime factorization method. Ex 6.3, 4 Find the square roots of the following numbers by the Prime Factorization Method. = 16 × 4 Thus, 400 = 2 × 2 × 2 × 2 × 5 × 5 = 20 (iii) Take one factor from pair. Square root represented by a the symbol ” √ ”, Now here we learn different methods for finding the square root. (vi) 9604 By prime Factorization, (It is general method for square root calculation). Square root through prime factorisation - law To find the square root of the given number through prime factorization method we follows the following steps: (i) First we divide the given number in to its prime factor. = 4 × 4 × 4

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